GATE 2017 ME (ME1) – Question 58

Casting, Forming and Joining Processes · Bulk forming and sheet forming, estimation of load · 2 marks · Numerical answer

A cylindrical cup 10 mm deep and 15 mm in diameter is drawn from a circular blank. Neglect thickness variation. Find blank diameter in mm, to two decimal places.

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Correct answer: 28.71 to 28.73

Explanation

Conservation of sheet volume with constant thickness reduces to conservation of area. Blank area is cup-bottom area plus sidewall area: $\pi D^2/4=\pi d^2/4+\pi dh$. Thus $D=\sqrt{d^2+4dh}=\sqrt{15^2+4(15)(10)}=\sqrt{825}=28.7228$ mm, rounding to 28.72 mm.

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